If a line is tangent to a circle at how many points does it interest the circle?

The intersection of a tangent to a circle and the circle is at exactly one point. Don't let a drawing fool you. In a drawing, it looks like there are several points of intersection, but keep in mind that a point has no dimensions, no length, width, or height, and a line has only length but no width. A drawing is just a representation of a point and a line, so we can see them.